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4 years ago

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you were planning to use a ceramic tile design in your new bathroom. The towels are blue and white equilateral triangle of you d

ecides arrange the blue tiles in a hexagonal shape as shown if the side of each tile measures 7 cm what were the exact area of each hexagonal shape

1 answer:

Sonja [21]4 years ago

7 0

I found the image that should have accompanied this problem.

Given:
equilateral triangle with sides that measures 7cm.
hexagonal shape meaning 6 sides or 6 equilateral triangles used.

Area of an equilateral triangle = √3/4 * a²
A = √3 /4 * (7cm)²
A = 1.73/4 * 49cm²
A = 21.20 cm²

21.20 cm² * 6 tiles = 127.20 cm² ARea of the hexagon.

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Answer:

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$V = 1.23245$

Step-by-step explanation:

Given

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$V = \pi \int\limits^a_b {R(x)^2} \, dx$

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$V = \pi \int\limits^a_b {R(x)^2} \, dx$

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$V = \pi \int\limits^a_b {R(x)^2} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {(\cos 2x)^2} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx$

Apply the following half angle trigonometry identity;

$\cos^2(x) = \frac{1}{2}[1 + \cos(2x)]$

So, we have:

$\cos^2(2x) = \frac{1}{2}[1 + \cos(2*2x)]$

$\cos^2(2x) = \frac{1}{2}[1 + \cos(4x)]$

Open bracket

$\cos^2(2x) = \frac{1}{2} + \frac{1}{2}\cos(4x)$

So, we have:

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {\cos^2 (2x)} \, dx$

$V = \pi \int\limits^{\frac{\pi}{4}}_0 {[\frac{1}{2} + \frac{1}{2}\cos(4x)]} \, dx$

Integrate

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$V = \pi ([\frac{\frac{\pi}{4}}{2} + \frac{1}{8}\sin(4*\frac{\pi}{4})])$

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